I'm afraid that usual transport connections in these areas go in the east-west direction and there are very limited possibilities to go north-south as you need (and these bus lines usually run only during summer/winter tourist seasons).
So the easiest way would be to hire a car in Krakow (travel time by car is under 4 hours).
By train, you would need to go all the way westwards to Zilina or Bohumin and then go back eastwards to Kosice, Humenne and then Medzilaborce, indeed this would take several transfers and 13 to 15 hours of travel time. You can see the route if you enter Krakow and Medzilaborce into the search engine of Deutsche Bahn:
Other possibility would be to take bus from Krakow to Zakopane, there arrange minibus transport to Slovak border - Lysa Polana, then continue with Slovak local bus line to Poprad and take train in Poprad (again towards Kosice-Humenne-Medzilaborce).
For route from Lysa Polana to Medzilaborce you can use this page:
(button to switch the page to English is in the lower right corner).
You need to enter "Tatr.Javorina,,Lysá Polana" as the departure point and Medzilaborce as the destination.
I hope this will help you a bit...
Are you wanting to go to the Andy Warhol museum? I made the pilgrimage there once about 20 years ago. Bizarre and a bit of an anticlimax.
Haha I read over your Warhol museum excursion..I eventually gave up on the idea, Im not going to rent a car in a country where I cant read the signs, and Im not going to sit on various trains for 15 hours. Too bad it's in such an obscure place, where ironically it doesnt even seem to be appreciated that much. Oh well!
Thanks for the read!
Things have been changed there a lot in this corner of the world. I would recommend to add Presov in the trip as you don't have so much stuff to do in Medzlaborce. If you are fan of Warhol, it's a must place to visit. You can grab a sense of his isolation in the American art scene.
Driving this region is quite easy as long as you have common sense for driving a car. Traffic signs are quite easy to understand.Edited: 10 November 2012, 15:34
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